Hello!
So, you want to get a phone that has a good battery life, that has many connectivity options, one that's good for games and one with a full QWERTY. And no bar phones? The "No bar phones" request narrows your selection down, but I think that I can still help.
First of all, remember that it's not always the phone that's expensive, but also the plan. A plan with all this would cost a lot, over 50 pounds a month for sure, so be careful. Now, it looks like your daughter wants a smartphone. Smartphones have more features than basic phones, like improved web browsing, Wifi and 3g, better cameras, email, better keypads, etc... So as you can see, they do things a lot better. Now, smartphones usually only come in bar factors, but there is one that doesn't.
It's the Blackberry Pearl Flip. It's a smartphone, but it's small, and shaped like a normal flip phone. Here's the web page to it:
http://uk.blackberry.com/devices/blackberrypearl8200/pearl_features.jsp
I don't live in the UK (Assuming that you live in London England), but I think that they offer it there. You said not to find one on Orange. I looked on Vodaphone and they said that they didn't carry it, but I think that O2 does. They sell the flip 8220. The 8220 doesn't feature 3G, but is does feature WiFi, so you can browse the web faster. It comes in many colours, it has a 1.3 mp camera, a trackball for better navigation, a battery that can last up to 14 days on standby (Or 4 hours of talk time), access to the Blackberry app world where she can get many games for free or for a fee, built in games, great web browsing on the go and a fair sized QW ER TY keyboard. Now, why did I spell QWERTY QW ER TY (with spaces every 2 letters)? It's because it uses Blackberry's Sure-Type key style (Or Compact QWERTY). It's the same as a normal QWERTY, but it has 2 letters per key. After about 15 minutes, it becomes very easy to use. I hate T9 and ABC keypads but I like QWERTY keypads, but I like small phones. This is where sure-type comes into play. It's used on smaller phones, and is very east to type with.
This phone isn't the best if you want to go overseas, but if you want a "World phone" (Optimized for overseas traveling) I'd recommend the Samsung Ace or the Blackberry tour. Unfortunately, these are both bar phones, and may not be what you're looking for.
I'd just like to make a final not to say that Blackberries aren't just for business. They make great phones for work, or play. The 8220 is more for play. Their Pearl, Pearl flip and Curve series are great fun.
I hope that I helped your daughter find a new phone!